The perimeters of two squares are 40 m and 96 m respectively. Find the perimeter of another square equal in area to the sum of the first two squares.

Let the sides of the two squares be ‘x’ m and ‘y’ m.

Given: Perimeter of square with side ‘x’ m = 40 m

We know, Perimeter of square = 4 × side

⇒ 40 = 4 × x

⇒ 4x = 40

Also, perimeter of square with side ‘y’ m = 96 m

⇒ 96 = 4 × y

⇒ 4y = 96

We know, area of a square = side²

⇒ Area of square 1 = x²

⇒ Area of square 1 = 10²

∴ Area of square 1 = 100 m²

Similarly, Area of square 2 = 24² = 576 m²

Now, it is given that there is another square whose area is equal to sum of areas of squares 1 and 2.

⇒ Area of new square = 100 + 576 = 676 m²

Let the side of this square be ‘s’ m.

⇒ s² = 676

So, side of the new square is 26 m.

We know Perimeter of square = 4 × side

⇒ Perimeter of new square = 4 × s

⇒ Perimeter of new square = 4 × 26 m

∴ Perimeter of new square = 104 m

Thus, the perimeter of the new square is 104 m.